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Aim: How do we use an arithmetic sequence to solve problems? (This formula is NOT on the Regents Reference Sheet)

At the end of the lesson, you will be able to...

1. define what is meant by an arithmetic sequence and a common difference
2. determine whether a a given sequence is an arithmetic sequence
3. determine the common difference, d, for the nth term of an arithmetic sequence
4. discover the formula for the nth term of an arithmetic sequence
5. explain how to to find a specified term of an arithmetic sequence
6. solve numeric, algebraic, and verbal problems using the relationship for an arithmetic sequence

Here are some things to look for in the video...

1. What is an arithmetic sequence?
2. Write the formula for an arithmetic sequence.


Video 1

Video 2

Classwork: Answer each of the following

1.For the arithmetic sequence 100, 97, 94, 91,... find
a. the common difference
b. the 20th term (Ans: a. -3, b. 43)

2. Scott is saving to buy a guitar. In the first week he put aside $42 that he received for his birthday, and in each of the following weeks, he added $8 to his savings. He needs $400 for the guitar that he wants. In which week will he have enough enough money tor the guitar? (Ans: 46th week)

3. The 4th term of an arithmetic sequence is 80 and the 12th term is 32.
a. What is the common difference?
b. What is the first term of the sequence? Ans: a. -6, b. 98)

Homework: Answer #3 - 15 odd, 21, 23

Arith_Sequences.JPG

Answers:

A-Arith_Seq.JPG


Journal entry: How can you tell if a sequence is an arithmetic sequence?